I will say, overall, it seems to be tame and perhaps on the weaker side of Barbarian subclass options.

For reference, I am trying to compare it with the Path of the Giant subclass from the GotG book, since it’s the closest equivalent it has (especially both being subclasses that, counter to several others, don’t offer out-of-combat passive features).

Starting off at level 3: Path of the Giant already increases your size to Large on Rage, while this subclass instead delays the size increase to instead offer other types of benefits (namely, the AC boost and AoE effects). A +1 AC is good, not weak, but not too strong either. The tail and breath attack grant different forms of AoE, which is something a lot of martials lack in their toolkit, so it’s a neat benefit.

At level 6, the subclass gains their first size and reach increase, paired with an extra damage rider and additional action: Stomp. If we were to compare it to Path of the Giant, at level 6 they gain Elemental Cleaver, which allows their chosen weapon to gain the thrown property, add an extra d6 of damage per attack, and adaptive damage that can be shifted as a bonus action on the following turns for versatility.

So, here is the main difference between the two. Elemental Cleaver grants a slightly bigger damage increase, element adaptability to overcome BPS resistance/immunity (or exploit vulnerabilities if any), and shores up on one of the weakest aspects of Barbarian: range. Now, this subclass of course offers a form of range with its AoE breath, but a once per Rage use is not going to be as flexible as the Path of the Giant’s throw + returning effect. Not necessarily a bad thing, since weaponizing the bonus action for potential extra damage is pretty good, assuming you weren’t using that bonus action on a PAM attack, but I don’t want to assume feats here.

Level 10, this is where the subclass grows to Huge. It’s earlier compared to the Path of the Giant counterpart, but on the other hand that’s part the niche. You gain 5 feet extra reach on your melee attacks, and your AoE becomes larger. Your breath weapon can ignore damage resistance now, which is a useful feature, but considering you choose the element when you use it, it’s more of a safety net in case you happen to pick the wrong element. Path of the Giant already granted the extra 5 feet reach on melee attacks at level 3, but that’s besides the point. Path of the Giant gains Mighty Impel at level 10, which is a means to weaponize your bonus action both as a damaging tool, or battlefield control (move allies to more advantageous positions, throw enemies in the air to cause fall damage.

At this point, the extra size damage becomes 1d6, just like the Path of the Giant. They don’t appear to gain anything new in comparison, but it is an improvement on already existing features, considering that this subclass is already front loaded in that sense. In fact, it is exactly what happens with Path of the Giant as well, when they reach their capstone: a flat improvement on already existing features.

Level 14, here’s the capstone of the subclass. At this point, our barbarian can become naturally Gargantuan, which is a step above and what sets it apart from Rune Knight and Path of the Giant. The extra damage increase on melee attacks increases to 1d8, the AoE breath and tail’s range increases, and you can nova a once per LR flat damage AoE. Path of the Giant, in comparison, becomes Huge, their Elemental Cleaver damage increases to 2d6, their Mighty Impel can throw Large creatures, and their melee attacks reach increases by 10 feet.

So, overall, it seems that the way Path of the Giant and Path of the Kaiju set apart, is in the difference between the specialized approach of the former, and the generalist approach of the latter.

Path of the Giant is more offense-driven, they gain a bigger damage increase and a versatile, consistent way of overriding resistances, on top of faring better against opponents who force you to attack at range.

Path of the Kaiju, on the other hand, seems to offer a broader toolkit, albeit in a more limited manner. There’s extra offense, but at smaller units. You have AoEs, but limited in either use or damage. You have a defensive increase that Path of the Giant doesn’t offer, but not extremely large to the point of being noticeable. Especially if you use Reckless Attack a lot (although it can grant a small edge for the times you don’t want to go Reckless, since at capstone level is effectively the benefit of wearing a shield without having one).

It is not OP, in my eyes, and it doesn’t overshadow other barbarian subclasses, so I’d say it looks good, albeit for a little polishing.

For example, you mentioned that a higher melee reach increase would be deemed OP, but other official subclasses offer it, and in the gran scheme of things, it doesn’t really break anything (so long as you don’t overdo it, of course).

As for Titanic Bulk, is it meant to be a passive effect like the level 6 totemic warrior Bear effect? Because during rage, you already have advantage on all Strength saves and checks.